High-dimensional geometry of cortical population activity. Marius Pachitariu University College London

Transcription

1 High-dimensional geometry of cortical population activity Marius Pachitariu University College London

2 Part I: introduction to the brave new world of large-scale neuroscience Part II: large-scale data preprocessing with Suite2p Part III: large-scale data analysis Visual stimulus responses Ongoing spontaneous activity Behaviorally-related activity

3 The brave new world of large-scale neuroscience* However, we are accelerating!!! 2017 prediction: 200 neurons Stevenson & Kording, 2011 *Gao and Ganguli, Current Opinion in Neurobiology 2015

4 Standard, 200 cell recordings

5 Zoomed out, multiplane imaging, 10,000 cell recordings 10x real time Conventional resonant 2p scope Hz / plane GCaMP6s in excitatory neurons (Ai94, EMX-Cre) Layers 2/3 and 4

6 2016, year of the mesoscopes Sofroniew et al, 2016, elife Chen et al, 2016, elife Stirman et al, 2016, Nature Methods Nadella et al, 2016, Nature Methods

7 2016, year of the mesoscopes 2017, year of the high-density probes Neuropixels probe 70 μm 384 channels digitized 960 sites 1 cm

8 Right now, we can record 1,000 neurons with electrodes 10,000 neurons with two-photon But why do we need to record so many neurons? Is it really necessary?

9 10,000 How do we make sense of this kind of data? dimensionality reduction data neuronsstimuli measure tuning to stimuli relate to behavior, decision-making, perception etc. then do statistics B x number of dimensions

10 Is cortical activity: Low dimensional? good for us we only need to record a subset of all neurons bad for the brain no room for complex computations, wasted neurons High dimensional? bad for us we need to record a LOT of neurons good for the brain complex computations, like object recognition in deep networks

11 Classical theories of visual cortex MOUNTCASTLE All neurons in a column encode the same quantity, redundantly BARLOW Cortex recodes into a high dimensional sparse code Bosking et al, 1997, J Neurosci Low dimensional input in few neurons Expansion Low dimensional dense code in many neurons Nonlinear transformation High dimensional sparse code Thalamocortical inputs Cortical membrane potentials Cortical spiking Barlow, Possible principles underlying the transformations of sensory messages, 1961

12 Is cortical activity low or high dimensional? Gao and Ganguli, Curr. Op. Neuro. 2015

13 10,000 neurons 100 neurons Is cortical activity low or high dimensional? Gao,,Ganguli, CoSyNe 2014 we cannot really know yet not enough recorded neurons, stimuli 100 trials data Our study we recorded 10,000 neurons we showed 3,000 stimuli long periods of spontaneous activity (2 hours) 2,800 stimuli data

14 Multiplane imaging in visual cortex of awake mice 10x real time Conventional resonant 2p scope Hz / plane GCaMP6s in excitatory neurons (Ai94, EMX-Cre) Layers 2/3 and 4

15 Suite2p pipeline

16 Cell detection model r k r k is the timecourse of pixel k = Λ ki f i + α k B kj n j + η i Λ ki is the weight of the ROI i onto pixel k f i is the timecourse of ROI i B kj is the weight of the background component j onto pixel k n j is the timecourse of background component j η is some noise, which we re going to model as Gaussian j

17 12,392 neurons Processed in 2 hours on a GPU by Suite2p

18 Registration

19 The effect of the background signal on fluorescence at the soma

20 Modelling the background signal is really important!!!

21 Graphical user interface for quality control

22 Comparing with the other major pipeline (Pnevmatikakis et al) we find more cells!

23 The activity of boutons (pre-synaptic terminals)

24 The activity of dendrites and spines (post-synaptic terminals)

25 Spike deconvolution C s = F s k 2 + λ L(sሻ F is the fluorescence of one cell k is the calcium response kernel s is the actual spike train λl s is a regularization penalty

26 We have >10,000 cells, now what?

27 Neural tuning to drifting gratings responses (test data) example neuron mean (12,392 neurons) 0.6 Gaussian fit sd = 11.4 deg 0.4 more examples degrees from preferred direction

28 Responses to visual stimuli 100 of 3,000 stimuli 9 of 3,000 stimuli 300 of 10,000 neurons data (presented twice over 2 hours)

29 Dimensionality estimation Neurons Neurons Stimuli Dimensions Stimuli data B x Linear model

30 explained variance more diverse stimuli = more dimensions Model (linear) data 32 directions 32 nat scenes B x 1 1 fraction number of dimensions number of dimensions

31 fraction Dimensionality of thousands of stimuli repeat 1 repeat 2 Model (linear) data x B compute signal variance fit model to each repeat unexplained variance = signal variance of residuals of model fit explained variance upper bound ~1, number of dimensions

32 Nonlinear dimensionality reduction Hypothetical scenario neuron Dimensionality is linear nonlinear neuron 1

33 Defining nonlinear dimensionality Ambient dimension: 3 Linear dimension: 2 Nonlinear dimension: 1

34 Nonlinear dimensionality reduction Model (linear) Model (nonlinear) linear nonlinear data f B x data = f(bx)

35 ~4x fewer dimensions in nonlinear model linear nonlinear 16 orientations 32 directions 32 nat scenes

36 2,800 natural images, repeated twice, ~4x fewer dimensions in nonlinear model Explained variance (%) 100 Linear model 95% Nonlinear model 95% Number of dimensions Number of dimensions

37 How can the nonlinear dimensionality be so much lower? response 16 orientations basis functions B linear nonlinear threshold rectified fit basis function reconstruction recorded neuron #3943 Number of dimensions orientation (deg) orientation (deg) orientation (deg)

38 Dimensionality is higher than predicted by filtering images Explained variance (%) 100 Linear model 95% Nonlinear model 95% 50 Gabor filters Gabor filters Number of dimensions Number of dimensions

39 Did we present enough stimuli? Explained variance (%) Dimensions to explain 95% variance 100 Linear model 95% Nonlinear model 50 more stimuli more stimuli Number of dimensions Number of dimensions 0 0 1,000 2,000 3,000 Number of stimuli Nope. No sign of saturation.

40 Did we record enough neurons? Explained variance (%) Dimensions to explain 95% variance 100 Linear model 95% Nonlinear model 50 more neurons more neurons Number of dimensions Number of dimensions 0 0 2,000 4,000 6,000 Number of neurons Nope. No sign of saturation.

41 The sensory cortex

42 What about spontaneous activity?

43 1,500 of 13,451 neurons during spontaneous activity 1,500 neurons 30 minutes

44 Top principal component Neurons Neurons Time data Dimensions B Time x Linear model Top principal component

45 Same neurons, reordered by first principal component 1,500 neurons PC1

46 The first principal component is the pupil 1,500 neurons Pupil area PC1

47 Non-negative matrix factorization (is kind of like clustering) Neurons Neurons Time data Dimensions B Time x Non-negative constraints B>0 X>0

48 Same neurons, organized into clusters 1,500 neurons

49 Pairwise spontaneous correlations are consistent Correlation matrices (10 out of 12,384 neurons) 1 st half of data 2 nd half of data How many dimensions of spontaneous activity account for the correlation matrix? similarity of matrices: 90.34% common variance

50 Decomposing the correlation matrix Neurons Neurons Neurons Neurons Dimensions Neurons Neurons Correlation matrix Dimensions B Neurons B T Two different time periods Time Dimensions Time Dimensions Time Z-score (data) B x 1 B x 2

51 10,000 neurons explained variance of the correlation matrix Spontaneous activity: dimensionality 20,000 timepoints data variance explained B x number of dimensions

52 Have we recorded enough neurons? Yes! increasing number of neurons

53 Does spontaneous activity resemble stimulus responses? Can we visualize them together? Kenet et al, Nature, 2003 Ringach, Curr Op Neurobiol 2009 Berkes et al, Science 2011 (and many more)

54 Visualizing together spontaneous and stimulus components neural component ν = vector in R N space 1. trial-averaged responses to a stimulus 2. principal component of spontaneous activity ν neurons time data component activity

55 Stimuli Stimuli Signal dimensions Spont dimensions 20 minutes

56 Summary of scientific results Stimulus-driven activity in visual cortex is high dimensional: >1,000 linear dimensions, >300 nonlinear dimensions, no sign of hitting a limit. Dimensionality is higher than predicted from image filtering. Consistent with the efficient coding hypothesis. Spontaneous activity in visual cortex is relatively low dimensional: ~50 dimensions, does not go up with increasing number of neurons Encodes behavioral state and reflects brain-wide activity Does not resemble stimulus-driven activity. Is uninterrupted by sensory activity

57 Acknowledgements Carsen Stringer Nick Steinmetz Matteo Carandini Kenneth Harris